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Bayesian nonparametric calibration and combination of predictive distributions

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We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights. Building on the work of Ranjan and Gneiting (2010) and Gneiting and Ranjan (2013), we use infinite beta mixtures for the calibration. The proposed Bayesian nonparametric approach takes advantage of the flexibility of Dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions. The inference procedure is based on Gibbs sampling and allows accounting for uncertainty in the number of mixture components, mixture weights, and calibration parameters. The weak posterior consistency of the Bayesian nonparametric calibration is provided under suitable conditions for unknown true density. We study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of daily S&P returns and daily maximum wind speed at the Frankfurt airport.

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  • Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2015. "Bayesian nonparametric calibration and combination of predictive distributions," Working Paper 2015/03, Norges Bank.
  • Handle: RePEc:bno:worpap:2015_03
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    Cited by:

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    3. Roberto Casarin & Giulia Mantoan & Francesco Ravazzolo, 2016. "Bayesian Calibration of Generalized Pools of Predictive Distributions," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-24, March.
    4. Roberto Casarin & Fausto Corradin & Francesco Ravazzolo & Nguyen Domenico Sartore & Wing-Keung Wong, 2020. "A Scoring Rule for Factor and Autoregressive Models Under Misspecification," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(2), pages 66-103, June.
    5. Tomasz Serafin & Bartosz Uniejewski & Rafał Weron, 2019. "Averaging Predictive Distributions Across Calibration Windows for Day-Ahead Electricity Price Forecasting," Energies, MDPI, Open Access Journal, vol. 12(13), pages 1-12, July.
    6. Barbara Rossi, 2019. "Forecasting in the Presence of Instabilities: How Do We Know Whether Models Predict Well and How to Improve Them," Working Papers 1162, Barcelona Graduate School of Economics.
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    8. Casarin, Roberto & Costola, Michele, 2019. "Structural changes in large economic datasets: A nonparametric homogeneity test," Economics Letters, Elsevier, vol. 176(C), pages 55-59.
    9. Knut Are Aastveit & James Mitchell & Francesco Ravazzolo & Herman van Dijk, 2018. "The Evolution of Forecast Density Combinations in Economics," Tinbergen Institute Discussion Papers 18-069/III, Tinbergen Institute.
    10. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2019. "Density Forecasting," BEMPS - Bozen Economics & Management Paper Series BEMPS59, Faculty of Economics and Management at the Free University of Bozen.

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    More about this item

    Keywords

    Forecast calibration; Forecast combination; Density forecast; Beta mixtures; Bayesian nonparametrics; Slice sampling.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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